Let's solve the given question step-by-step using the equation [tex]\( Y = 2X + 1 \)[/tex]. We need to calculate the value of [tex]\( Y \)[/tex] for each given value of [tex]\( X \)[/tex]:
1. When [tex]\( X = 1 \)[/tex]:
[tex]\[
Y = 2(1) + 1 = 2 + 1 = 3
\][/tex]
So, [tex]\( Y = 3 \)[/tex].
2. When [tex]\( X = 2 \)[/tex]:
[tex]\[
Y = 2(2) + 1 = 4 + 1 = 5
\][/tex]
So, [tex]\( Y = 5 \)[/tex].
3. When [tex]\( X = 3 \)[/tex]:
[tex]\[
Y = 2(3) + 1 = 6 + 1 = 7
\][/tex]
So, [tex]\( Y = 7 \)[/tex].
4. When [tex]\( X = 0 \)[/tex]:
[tex]\[
Y = 2(0) + 1 = 0 + 1 = 1
\][/tex]
So, [tex]\( Y = 1 \)[/tex].
5. When [tex]\( X = -1 \)[/tex]:
[tex]\[
Y = 2(-1) + 1 = -2 + 1 = -1
\][/tex]
So, [tex]\( Y = -1 \)[/tex].
6. When [tex]\( X = -2 \)[/tex]:
[tex]\[
Y = 2(-2) + 1 = -4 + 1 = -3
\][/tex]
So, [tex]\( Y = -3 \)[/tex].
Now, let's fill in our table with the calculated values of [tex]\( Y \)[/tex]:
[tex]\[
\begin{tabular}{r|l}
$X$ & $Y=2 X+1$ \\
\hline
1 & 3 \\
2 & 5 \\
3 & 7 \\
0 & 1 \\
-1 & -1 \\
-2 & -3 \\
\end{tabular}
\][/tex]
So, the final values of [tex]\( Y \)[/tex] for the given [tex]\( X \)[/tex] values are [tex]\( 3, 5, 7, 1, -1, \)[/tex] and [tex]\( -3 \)[/tex].
